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Mariulka [41]
3 years ago
5

A 0.311 kg tennis racket moving 30.3 m/s east makes an elastic collision with a 0.0570 kg ball moving 19.2 m/s west. Find the ve

locity of the tennis racket after the collision.

Mathematics
1 answer:
max2010maxim [7]3 years ago
5 0

<u>Answer</u>:

The velocity of the tennis racket after the collision 14.966 m/s.

<u>Step-by-step explanation:</u>

An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies remains the same.

So, the total kinetic energy before collision = the total kinetic energy after collision.

For the given problem let the following:

m₁ = mass of tennis racket = 0.311 kg

m₂ = mass of the ball = 0.057 kg

u₁ = velocity of tennis racket before collision = 30.3 m/s

u₂ = velocity of the ball before collision = -19.2 m/s

v₁ = velocity of tennis racket after collision

v₂ = velocity of the ball after collision

Right ⇒east  (+) , Left⇒ west (-)

v₁ = [ u₁ * (m₁ - m₂) + u₂ * 2m₂ ]/ (m₁ + m₂)

  = ( 30.3 * (0.311 - 0.057) - 19.2 * 2 * 0.057 ) / ( 0.311 + 0.057)

  = 14.966 m/s.

So, the velocity of the tennis racket after the collision 14.966 m/s.

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Step-by-step explanation:

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Answer:

a) For this case we can conclude that we are 95% confident that the true mean for the variable of interest is between 3.4 and 4.24 days in the US population.

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Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

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The confidence interval for the mean is given by the following formula:

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For the 95% confidence interval the value of \alpha=1-0.95=0.05 and \alpha/2=0.025, with that value we can find the quantile required for the interval in the normal standard distribution.

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The confidence interval after apply the formulas was (3.40 ,4.24)

Part a

For this case we can conclude that we are 95% confident that the true mean for the variable of interest is between 3.4 and 4.24 days in the US population.

Part b

The 95% confident means that if we select 100 different samples and calculate the 95% confidence interval for each sample selected, then we will have approximately 95 out of 100 confidence intervals will contain the true mean for the parameter of interest.

Part c

If we have the same info but we want more confidence that implies that the confidence interval would be wider, since the margin of erroe increase with more confidence, because the critical value increase.

Part d

We need to take in count that the margin of error is given by:

ME=t_{\alpha/2}\frac{s}{\sqrt{n}}

Assuming that we have the same confidence level and the value for the deviation s not changes. If we see if we decrease the sample size, then the margin of error would be lower since the original sample size was 1151. So then if we use 500 Americans we would have a lower value for the margin of error for this new interval. And then our confidence interval would smaller than the original.  

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